I had a similar problem and discovered that the network card on the pi was going to sleep to save power. Since I ssh into my pi, that was hard to figure out, but adding a cron task to ping the router fixed it.

Does the plex server works properly?
I installed it on the RaspberryPi but unfortunately, I never managed to watch a full movie in good conditions.
The Pi wasn't powerful enough to display the media (video file).

I use my pi as an emby server emby.media/ for my home media in conjunction with my Roku. I've loved it for the past two years. My wife says I've spoiled her into never touching our Blu Rays/DVDs ever again.

I've got a few myself! One I've been using for years as a torrent server. I've got it hooked up to a router and NAS drive at home, then I've got a folder action on my laptop that automatically sends any .torrent files to the pi which automatically downloads them to the NAS drive for later use. It's useful in case I'm somewhere that's blocking P2P traffic.

The other one I set up at work with a couple sensors to monitor our bathroom and post whether it's occupied or not to a slack channel. I'm working on a backend for it right now for slash commands so people can make reservations 😂

If you have a RaspberryPi, the very first thing you should install on it is Syncthing.
It will then allow you to have a personnal Dropbox installed.
I connected a 3To HDD on it and boom I have a 3To of cloud.

When you have this, the possibilities are endless.
Let's consider that you have Syncthing installed and configured on all your devices:

You can export your photos in a specific folder on your computer and boom they're saved automatically on your HDD.

I have Boosnote installed on my machines. With Synchting and Boostnote, I have a Evernote, Google Keep, etc, that is synchronized but not shared with any company. Everything is my property. :-)

I have a Plex server on my Shield that is connected over the air to my RaspberryPi. So it serves the content, videos, photos (synchronized automatically from earlier). So as soon as you finished working on your photos, you export them on a folder on your computer and after a few minutes (Syncthing is soo fast), you can enjoy them on your TV and even your relatives from the other side of the world can enjoy.
You have nothing to do.

As you can see, I am very enthusiastic about that piece of software. :-)

But Syncthing is absolutely fantastic, open source, free and I could definitely not get rid of it and my RaspberryPi.
It cost the price of a one year Dropbox subscription for three times the volume and it works from 4 years now, like clockwork. :-)

I currently have a Pi3B+ running FreeBSD 12, 3x USB thumbdrives in a RAID-Z1 configuration, running several jails, also running ZeroTier for personal VPN access. This little toy is awesome, I use it when I need remote access to something while I'm off-site, since I can just SSH into it via ZeroTier, and then SSH from there into other machines in my network.

RAID-Z1 is similar to a normal RAID-5 setup for redundancy, but with the added benefit of it being ZFS based. This means things like instant snapshotting, creating virtual block devices (for VMs or iSCSI), and all the neatness of SEND/RECV to transfer entire file systems between machines. ZFS also is one of the few file systems that not only hashes every single block on the storage device, it also VERIFIES the block against the hash tree on EVERY read operation, ensuring data integrity (instead of waiting for total failure or SMART faults)

1) Install ZeroTier on a laptop.
2) Then install ZeroTier on a Pi.
3) Have the Pi sitting at home. Take the laptop out of the house (I travel frequently, so this is normal for me).
4) Use the Pi's ZT address to SSH into it from the laptop.
5) While inside of the Pi's SSH session, use THAT to SSH into other nodes on the Pi's LAN.

I also use a Yubikey with PuTTY for SSH authentication. PuTTY supports agent forwarding, so my Yubikey will also allow authentication to other nodes within the network.

I build a small train information panel. This grabs the real train Infos from a particular trainstation and displays that onto a LCD display. This was build for my sons Modell train. There is a little bit hardware knowledge and programing skills needed.

Considering the amount of electricity it used, it was perfect for running Kodi (media centre), and we also had it connected to a VPN to download, well, things... The only reason I upgraded to a proper NUC in the end was because the Pi doesn't support decoding x265 HEVC footage in real time, which was a major set back for me personally.

I just purchased one myself and have it setup with both Raspberian and Windows 10 IoT. I'm still not sure which direction to take my learning with it. I'm a lot more comfortable with the Microsoft way of doing things (Windows, C#, etc) but the Raspberian experience feels more like a regular computer experience, plus I would expand my knowledge more by learning Java in depth.

I will probably eventually get into some hardware related stuff, both for my guitar/music hobby and perhaps for my work in supporting manufacturing operations.

I have RP3 for use with Kodi media center, running transmission torrent client as well with web-UI so i can connect and add torrent files.
Also uses it to download twitter sample firehose archives created by Twitark

I have another RP2 that i use as a home camera when i am away which uses MotionEYE OS
Installed with Node-Red integrated with PushBullet channels, so i can 'Alarm' and it will send me notifications, or turn it off when i am at home.

Lastly i have a RPZero with Led pHat from pimoroni which is for visualizations.

I‘ve ordered an octo soundcard from audio injector for my pi2 (only hardware stuff I did) and wrote some nodejs scripts to turn it into a really good working sound system with capabilities of playing old tapes and vinyl from my 30 year old hifi system and stream it to wireless speakers all around the house (with airplay support, which stops the current playback on play and after that, my hifi system will stream again, good for parties, where someone wants to show a video to the crowd or wants to play a favorite song in between good ol‘ tapes 😁

I use my pi to run Home Assistant so my pi acts as a bridge between all the smart devices in my house from my smart slow cooker, lights, TV, to my climate control, Google Home, and even my automated cat feeder!

When I got my first Raspberry Pi I used it to build a Twitter bot with Python because I wanted to learn the language. You can find the bot on Twitter: twitter.com/socrabot_ It finds and retweets the most interesting stuff about Software Craftsmanship.

I also wrote a blog post on how I did it. It might help you to get started :)

I don't have a Pi3, I have an Odroid XU4, but they're kinda similar. I use mine in conjunction with a NAS as a bitcoin and litecoin node and I've been thinking about setting it up as a Wireguard VPN, so I can connect to the internet via home when I'm away,

site-to-site vpn adapters, HTPC with OpenElec, 3d-printer controller with Octoprint, one ntp enables my alarm clock so that I don't have to set it during DST, Ubiquiti wifi-controller, IoT enabling my height-adjustable desk. I also have an x-mas tree with rgb leds controller by a pi :)

I don't own a Pi. However I do have an Odroid-C1 (very similar).
It's served me as a Kodi TV box (Linux), and an Android device (Mostly to run Android games). I've also used it as a gaming console with Lakka.

It's currently being used as a Lyrics/Chord display for musicians at church on a floor monitor.

I’m intrigued whether I could run one of these with an external keyboard and mouse, with HDMI monitor, to code node and react systems on a Linux install? Preferably in VS code. Do they have the power to handle this?

I use my Raspberry Pi 2 to play music from a USB stick with mpd & icecast2 to my internet radio or analyse my internet traffic with ntopng and a script to use the FritzBox capture feature, so I can watch in near realtime which servers my devices are connecting to.